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5.9

5.9. Show that a Quad. is a Parallel. B. C. A. D. Theorem 5.22. sides. If both pairs of opposite ________ of a quadrilateral are congruent, then the quadrilateral is a parallelogram. then ABCD is a parallelogram. 5.9. Show that a Quad. is a Parallel. B. C. A. D. Theorem 5.23.

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5.9

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  1. 5.9 Show that a Quad. is a Parallel. B C A D Theorem 5.22 sides If both pairs of opposite ________ of a quadrilateral are congruent, then the quadrilateral is a parallelogram. then ABCD is a parallelogram.

  2. 5.9 Show that a Quad. is a Parallel. B C A D Theorem 5.23 angles If both pairs of opposite ________ of a quadrilateral are congruent, then the quadrilateral is a parallelogram. then ABCD is a parallelogram.

  3. 5.9 Show that a Quad. is a Parallel. B C A D Theorem 5.24 If one pair of opposite sides of a quadrilateral are __________ and ________, then the quadrilateral is a parallelogram. congruent parallel then ABCD is a parallelogram.

  4. 5.9 Show that a Quad. is a Parallel. B C A D Theorem 5.25 If the diagonals of a quadrilateral ______ each other, then the quadrilateral is a parallelogram. bisect then ABCD is a parallelogram.

  5. 5.9 Show that a Quad. is a Parallel. B A D C Identify parallelograms Example 1 Explain how you know that quadrilateral ABCD is a parallelogram. a. Corollary to Theorem 5.16 By the _____________________________ you know that congruent Because both pairs of opposite angles are ___________, Theorem 5.23 then ABCD is a parallelogram by ______________.

  6. 5.9 Show that a Quad. is a Parallel. B A E C D Identify parallelograms Example 1 Explain how you know that quadrilateral ABCD is a parallelogram. b. EC ED In the diagram AE = ____ and BE = ____. So, the diagonals bisect each other, Theorem 5.25 and ABCD is a parallelogram by ______________.

  7. 5.9 Show that a Quad. is a Parallel. • In quadrilateral GHJK, What theorem can you use to show that GHJK is a parallelogram. J H G K Checkpoint. Complete the following exercises. Theorem 5.23 shows that GHJK is a parallelogram.

  8. 5.9 Show that a Quad. is a Parallel. Q P By Theorem 5.25, if the diagonals of PQRS ______ each other, then it is a parallelogram. You are given that R T S Use algebra with parallelograms Example 2 For what value of x is quadrilateral PQRS a parallelogram? bisect Set the segment lengths equal. Substitute for PT and for _____. Subtract ____ from both sides. Divide each side by ____ . Quadrilateral PQRS is a parallelogram when x = ___.

  9. 5.9 Show that a Quad. is a Parallel. F G D H Checkpoint. Complete the following exercises. • For what value of x is quadrilateral DFGH a parallelogram.

  10. 5.9 Show that a Quad. is a Parallel. Use coordinate geometry Example 3 Show that quadrilateral KLMN is a parallelogram? One way is to show that a pair of sides are congruent and parallel. Then apply ________________. Theorem 5.24 First use the Distance Formula to show that KL and MN are ____________. congruent

  11. 5.9 Show that a Quad. is a Parallel. Use coordinate geometry Example 3 Show that quadrilateral KLMN is a parallelogram? Then use the slope formula to show that KL ____ MN. parallel KL and MN have the same slope, so they are _________. KL and MN are congruent and parallel. So, KLMN is a parallelogram by __________________. Theorem 5.24

  12. 5.9 Show that a Quad. is a Parallel. Checkpoint. Complete the following exercises. • Explain another method that can be used to show that quadrilateral KLMN in Example 3 is a parallelogram. Draw the diagonals and find the point of intersection. Show that the diagonals bisect each other using Distance Formula. Apply Theorem 5.25.

  13. 5.9 Show that a Quad. is a Parallel. Pg. 324, 5.9 #2-22 even

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